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Nonparametric estimation of non-stationary velocity fields from 3D particle tracking velocimetry data


  • Kohler, Michael
  • Krzyżak, Adam


Nonparametric estimation of nonstationary velocity fields from 3D particle tracking velocimetry data is considered. The velocities of tracer particles are computed from their positions measured experimentally with random errors by high-speed cameras observing turbulent flows in fluids. Thus captured discrete data is plugged into a smoothing spline estimate which is used to estimate the velocity field at arbitrary points. The estimate is further smoothed over several time frames using the fixed design kernel regression estimate. Consistency of the resulting estimate is investigated. Its performance is validated on the real data obtained by measuring a fluid flow of a liquid in a (rotating) square tank agitated by an oscillating grid.

Suggested Citation

  • Kohler, Michael & Krzyżak, Adam, 2012. "Nonparametric estimation of non-stationary velocity fields from 3D particle tracking velocimetry data," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 1566-1580.
  • Handle: RePEc:eee:csdana:v:56:y:2012:i:6:p:1566-1580
    DOI: 10.1016/j.csda.2011.09.025

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    References listed on IDEAS

    1. Zhao, L. C., 1987. "Exponential bounds of mean error for the nearest neighbor estimates of regression functions," Journal of Multivariate Analysis, Elsevier, vol. 21(1), pages 168-178, February.
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    Cited by:

    1. Hertel, Ida & Kohler, Michael, 2013. "Estimation of the optimal design of a nonlinear parametric regression problem via Monte Carlo experiments," Computational Statistics & Data Analysis, Elsevier, vol. 59(C), pages 1-12.


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